First published in 1982. These lectures are in two parts. Part I, entitled injective Modules
Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E, R) …

INTRODUCTION In the broadest sense, this is a study of commutative rings which satisfy the
(finitely) pseudo-Frobenius (or (F) PF) condition: All (finitely generated) faithful modules …

1. Introduction, In this paper we prove several theorems about rings having a generous
supply of projective injective modules. This is a curious class of rings. For instance, every …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …

Lntroduction It is easily seen that if an R-module is a generator in the category mod-R, then it
is faithful. However, the converse is not necessarily true. Naturally one is led to ask for which …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

This is the first book on the subject of FPF rings and the systematic use of the notion of the
generator of the category mod-R of all right R-modules and its relationship to faithful …

Let R be a ring with identity 1. We denote the category of unital right (respectively left) R-
modules by 'U&m). MR will signify ME YJl&M E $ tJl). We will be concerned with certain …